Math Is Fun Forum

I think Cantor made a real mess of this field. In mapping the counting numbers (proportional to some finite limit N) to the rational numbers (proportional to the finite limite N²) he made infinity impossible to understand in logical terms. Because it is infinity, that doesn't make everything magically correct. You should be able to think of infinity as some value N which is CONSISTENTLY increased without restriction. He insisted on increasing N inconsistently and therefore came up with some rather foolish results.

Here is how I do it:
http://lesliegreen.byethost3.com/articles/new_maths.pdf